Derivation of particular solutions using chebyshev polynomial based functions

International Journal of Computational Methods

Volumn 4, Issue 1, 2007, Pages 15-32

  Chen, C S ^a   Lee, Sungwook ^a   Huang, C S ^b  

^a University of Southern Mississippi   (United States)

^b NATIONAL SUN YAT SEN UNIVERSITY   (Taiwan)

Author keywords

Chebyshev polynomial; Meshless methods; Method of fundamental solutions; Multidimensional interpolation; Particular solution; Radial basis functions

Indexed keywords

CHEBYSHEV APPROXIMATION; COMPUTATIONAL METHODS; HELMHOLTZ EQUATION; INTERPOLATION; NUMERICAL METHODS; POLYNOMIALS;

CHEBYSHEV POLYNOMIAL; MESHLESS METHODS; MULTIDIMENSIONAL INTERPOLATION; RADIAL BASIS FUNCTIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 34547770712     PISSN: 02198762     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219876207001096     Document Type: Article

References (19)

1. Atkinson, K. E. [1985] The numerical evaluation of particular solutions for Poisson's equation, IMA J. Numer. Anal. 5, 319-338.
2. Bernardi, C. and Maday, Y. [1997] Spectral methods, in Handbook of Numerical Analysis, V, eds. Ciarlet, P. G. and Lions, J.-L. (Elsevier), pp. 209-485.
3. Boyd, J. P. [2001] Chebyshev and Fourier Spectral Methods (Dover, New York).
4. Burden, R. L. and Faires, J. D. [2005] Numerical Analysis, 8th edition (Thomson Brooks/Cole).
5. Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A. [1988] Spectral Methods in Fluid Dynamics (Springer-Verlag, New York).
6. Chen, C. S., Muleshkov, A. S., Golberg, M. A. and Mattheij, R. M. M. [2005] A mesh free approach to solving the axisymmetric Poisson's equation, Numer. Methods Partial Differential Equations 21, 349-367.
7. Chen, W. [2002] Symmetric boundary knot method, Eng. Anal. Boundary Elements 26(6), 489-494
8. Cheng, A. H.-D., Lafe, O. and Grilli, S. [1994] Dual reciprocity BEM based on global interpolation functions, Eng. Analy. Boundary Elements 13, 303-311.
9. Fairweather, G. and Karageorghis, A. [1998] The method of fundamental solution for elliptic boundary value problems, Adv. Coutput. Math. 9, 69-95.
10. Golberg, M. A. and Chen, C. S. [1998] The method of fundamental solutions for potential, Helmholtz and diffusion problems, in Boundary integral Methods - Numerical and Mathematical Aspects, ed. Golberg, M. A., Computational Mechanics Publications, pp. 103-176.
11. Golberg, M. A., Muleshkov, A. S., Chen, C. S. and Cheng, A. D.-H. [2003] Polynomial particular solutions for some partial differential operators, Numer. Methods Partial Differential Equations 19, 112-133.
12. Hon, Y. C. and Wu, Z. [2000] A quasi-interpolation method for solving stiff ordinary differential equations, Int. J. Numer. Methods Eng. 48, 1187-1197.
13. Hokwon, A. Cho, Golberg, M. A., Muleshkov, A. S. and Xin Li [2004] Trefftz methods for time dependent partial differential equations, CMC 1, 1-37.
14. Li, X. and Chen, C. S. [2004] A mesh-free method using hyperinterpolation and fast Fourier transform for solving differential equation, Eng. Anal. Boundary Elements 28, 1253-1260.
15. Muleshkov, A. S., Golberg, M. A. and Chen, C. S. [1999] Particular solutions of Helmholtz-type operators using higher order polyharmonic splines, Comput. Mech. 24, 411-419.
16. Muleshkov, A. S., Cher., C. S., Golberg, M. A. and Cheng, A. H.-D. [2000] Analytic particular solutions for inhomogeneous Helmholtz-type equations, Adv. Comput. Eng. Sci. eds. Atluri, S. N. and Brust, F. W., Tech Science Press, 1, 27-32.
17. Muleshkov, A. S., Golberg, M. A., Cheng, A. H.-D. and Chen, C. S. [2002] Polynomial particular solutions for Poisson problems, Boundary Elements XXIV, eds. Brebbia, C. A., Tadeu, A. and Popov, V., WIT Press, Southampton, Boston, 115-124.
18. Partridge, P. W., Brebbia, C. A. and Wrobel, L. C. [1992] The Dual Reciprocity Boundary Element Methods (Computational Mechanics Publications, Southampton, UK).
19. Tyn, M.-U. [1980] Partial Differential Equations of Mathematical Physics (North Holland, New York).